MUSA508 Midterm: Miami Home Price Prediction Markdown
Julian Hartwell & Juliana Zhou
October 19, 2020
## Reading layer `studentsData' from data source `/Users/julianazhou/Documents/GitHub/Miami/studentsData.geojson' using driver `GeoJSON'
## Simple feature collection with 3503 features and 58 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: -80.31756 ymin: 25.70911 xmax: -80.12061 ymax: 25.87091
## geographic CRS: WGS 84## Reading layer `Municipality_poly' from data source `https://opendata.arcgis.com/datasets/5ece0745e24b4617a49f2e098df8117f_0.geojson' using driver `GeoJSON'
## Simple feature collection with 78 features and 11 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: -80.87358 ymin: 25.13742 xmax: -80.04276 ymax: 25.97944
## geographic CRS: WGS 84## Reading layer `Shoreline' from data source `https://opendata.arcgis.com/datasets/58386199cc234518822e5f34f65eb713_0.geojson' using driver `GeoJSON'
## Simple feature collection with 1628 features and 6 fields
## geometry type: MULTILINESTRING
## dimension: XY
## bbox: xmin: -80.85817 ymin: 25.00041 xmax: -80.11807 ymax: 25.97517
## geographic CRS: WGS 84##
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|======================================================================| 100%## Reading layer `MiddleAttendanceBoundary' from data source `https://opendata.arcgis.com/datasets/dd2719ff6105463187197165a9c8dd5c_0.geojson' using driver `GeoJSON'
## Simple feature collection with 54 features and 17 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: -80.67463 ymin: 25.37431 xmax: -80.11807 ymax: 25.97515
## geographic CRS: WGS 84Reg1 <- lm(miamiHomes.train$SalePrice ~ ., data = miamiHomes.train %>%
st_drop_geometry() %>%
dplyr::select(Shore1, MedHHInc, TotalPop, MedRent, pctWhite, pctPoverty,
Brownsville.MS, CitrusGrove.MS, JosedeDiego.MS, GeorgiaJA.MS,
KinlochPk.MS, Madison.MS, Nautilus.MS, Shenandoah.MS, WestMiami.MS,))
Reg2 <- lm(miamiHomes.train$SalePrice ~ ., data = miamiHomes.train %>%
st_drop_geometry() %>%
dplyr::select(-GEOID, -ID, -toPredict))
summary(Reg1)##
## Call:
## lm(formula = miamiHomes.train$SalePrice ~ ., data = miamiHomes.train %>%
## st_drop_geometry() %>% dplyr::select(Shore1, MedHHInc, TotalPop,
## MedRent, pctWhite, pctPoverty, Brownsville.MS, CitrusGrove.MS,
## JosedeDiego.MS, GeorgiaJA.MS, KinlochPk.MS, Madison.MS, Nautilus.MS,
## Shenandoah.MS, WestMiami.MS, ))
##
## Residuals:
## Min 1Q Median 3Q Max
## -505816 -63281 -6461 49079 692032
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 274559.3516 50967.1119 5.387 0.00000008255 ***
## Shore1 -5.7452 1.2288 -4.676 0.00000318341 ***
## MedHHInc 1.3698 0.2344 5.844 0.00000000620 ***
## TotalPop 4.4526 1.7971 2.478 0.01333 *
## MedRent 8.0105 16.9273 0.473 0.63611
## pctWhite 87738.7535 21213.9059 4.136 0.00003722772 ***
## pctPoverty -65160.5762 46955.0564 -1.388 0.16542
## Brownsville.MS -74321.8984 35665.2339 -2.084 0.03733 *
## CitrusGrove.MS -63085.3758 33757.2289 -1.869 0.06184 .
## JosedeDiego.MS -24574.0248 36087.1737 -0.681 0.49600
## GeorgiaJA.MS -83659.5425 33968.4429 -2.463 0.01389 *
## KinlochPk.MS -20898.1255 23871.5518 -0.875 0.38147
## Madison.MS -102752.0450 89066.6696 -1.154 0.24882
## Nautilus.MS 229234.0043 37774.8118 6.068 0.00000000162 ***
## Shenandoah.MS 99482.5601 31097.1370 3.199 0.00141 **
## WestMiami.MS NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 113700 on 1569 degrees of freedom
## (482 observations deleted due to missingness)
## Multiple R-squared: 0.6029, Adjusted R-squared: 0.5994
## F-statistic: 170.2 on 14 and 1569 DF, p-value: < 0.00000000000000022summary(Reg2)##
## Call:
## lm(formula = miamiHomes.train$SalePrice ~ ., data = miamiHomes.train %>%
## st_drop_geometry() %>% dplyr::select(-GEOID, -ID, -toPredict))
##
## Residuals:
## Min 1Q Median 3Q Max
## -633041 -52563 -324 44778 716398
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) -5246.4350534539 142697.2837201184 -0.037
## Folio 0.0000000852 0.0000010166 0.084
## Property.CityMiami Beach 220589.4402736548 102729.5109330711 2.147
## LotSize 17.9744511198 1.6598697438 10.829
## Bed 8653.6103385339 4483.3273688662 1.930
## Bath 4613.3433411990 5440.1497794038 0.848
## Stories 13854.9186849976 11214.3749333794 1.235
## Pool 77281.6482034501 9820.8922735323 7.869
## Fence -149.0504182702 5646.3493174582 -0.026
## Patio 4073.1199787392 5115.9393321635 0.796
## ActualSqFt 67.0325323507 6.2306983088 10.758
## Age -698.9747848495 147.1481424575 -4.750
## Shore1 -3.3692430543 1.0299999168 -3.271
## MedHHInc 1.0907134061 0.1933144376 5.642
## TotalPop 3.3995118427 1.4813680114 2.295
## MedRent 10.1107571325 13.9704575462 0.724
## pctWhite 72584.5891876008 18038.4043269414 4.024
## pctPoverty -28329.3231192995 38669.4205943405 -0.733
## Brownsville.MS -19595.1411441002 29848.9697522498 -0.656
## CitrusGrove.MS -16536.9740318180 27908.0093871838 -0.593
## JosedeDiego.MS 41689.6871928630 30171.4322819578 1.382
## GeorgiaJA.MS -21745.7906222292 28569.9668882082 -0.761
## KinlochPk.MS 7151.5470039981 19733.8734794334 0.362
## Madison.MS -24901.9379151104 73254.8959734925 -0.340
## Nautilus.MS NA NA NA
## Shenandoah.MS 122292.1069263248 25991.1247964894 4.705
## WestMiami.MS NA NA NA
## Pr(>|t|)
## (Intercept) 0.97068
## Folio 0.93322
## Property.CityMiami Beach 0.03192 *
## LotSize < 0.0000000000000002 ***
## Bed 0.05377 .
## Bath 0.39656
## Stories 0.21685
## Pool 0.00000000000000663 ***
## Fence 0.97894
## Patio 0.42606
## ActualSqFt < 0.0000000000000002 ***
## Age 0.00000221955735896 ***
## Shore1 0.00109 **
## MedHHInc 0.00000001990953696 ***
## TotalPop 0.02187 *
## MedRent 0.46934
## pctWhite 0.00005998767470287 ***
## pctPoverty 0.46391
## Brownsville.MS 0.51161
## CitrusGrove.MS 0.55357
## JosedeDiego.MS 0.16724
## GeorgiaJA.MS 0.44669
## KinlochPk.MS 0.71710
## Madison.MS 0.73395
## Nautilus.MS NA
## Shenandoah.MS 0.00000276128964864 ***
## WestMiami.MS NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 93070 on 1559 degrees of freedom
## (482 observations deleted due to missingness)
## Multiple R-squared: 0.7358, Adjusted R-squared: 0.7318
## F-statistic: 180.9 on 24 and 1559 DF, p-value: < 0.00000000000000022summ(Reg1)| Observations | 1584 (482 missing obs. deleted) |
| Dependent variable | miamiHomes.train$SalePrice |
| Type | OLS linear regression |
| F(14,1569) | 170.16 |
| R² | 0.60 |
| Adj. R² | 0.60 |
| Est. | S.E. | t val. | p | |
|---|---|---|---|---|
| (Intercept) | 274559.35 | 50967.11 | 5.39 | 0.00 |
| Shore1 | -5.75 | 1.23 | -4.68 | 0.00 |
| MedHHInc | 1.37 | 0.23 | 5.84 | 0.00 |
| TotalPop | 4.45 | 1.80 | 2.48 | 0.01 |
| MedRent | 8.01 | 16.93 | 0.47 | 0.64 |
| pctWhite | 87738.75 | 21213.91 | 4.14 | 0.00 |
| pctPoverty | -65160.58 | 46955.06 | -1.39 | 0.17 |
| Brownsville.MS | -74321.90 | 35665.23 | -2.08 | 0.04 |
| CitrusGrove.MS | -63085.38 | 33757.23 | -1.87 | 0.06 |
| JosedeDiego.MS | -24574.02 | 36087.17 | -0.68 | 0.50 |
| GeorgiaJA.MS | -83659.54 | 33968.44 | -2.46 | 0.01 |
| KinlochPk.MS | -20898.13 | 23871.55 | -0.88 | 0.38 |
| Madison.MS | -102752.05 | 89066.67 | -1.15 | 0.25 |
| Nautilus.MS | 229234.00 | 37774.81 | 6.07 | 0.00 |
| Shenandoah.MS | 99482.56 | 31097.14 | 3.20 | 0.00 |
| WestMiami.MS | NA | NA | NA | NA |
| Standard errors: OLS |
stargazer(Reg1, Reg2, title="Training Set LM Results", align=TRUE, type = "html", out = "Regression_Results.htm")##
## <table style="text-align:center"><caption><strong>Training Set LM Results</strong></caption>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td colspan="2"><em>Dependent variable:</em></td></tr>
## <tr><td></td><td colspan="2" style="border-bottom: 1px solid black"></td></tr>
## <tr><td style="text-align:left"></td><td colspan="2">SalePrice</td></tr>
## <tr><td style="text-align:left"></td><td>(1)</td><td>(2)</td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Folio</td><td></td><td>0.00000</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(0.00000)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Property.CityMiami Beach</td><td></td><td>220,589.400<sup>**</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(102,729.500)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">LotSize</td><td></td><td>17.974<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(1.660)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Bed</td><td></td><td>8,653.610<sup>*</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(4,483.327)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Bath</td><td></td><td>4,613.343</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(5,440.150)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Stories</td><td></td><td>13,854.920</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(11,214.380)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Pool</td><td></td><td>77,281.650<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(9,820.892)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Fence</td><td></td><td>-149.050</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(5,646.349)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Patio</td><td></td><td>4,073.120</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(5,115.939)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">ActualSqFt</td><td></td><td>67.033<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(6.231)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Age</td><td></td><td>-698.975<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(147.148)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Shore1</td><td>-5.745<sup>***</sup></td><td>-3.369<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(1.229)</td><td>(1.030)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">MedHHInc</td><td>1.370<sup>***</sup></td><td>1.091<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(0.234)</td><td>(0.193)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">TotalPop</td><td>4.453<sup>**</sup></td><td>3.400<sup>**</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(1.797)</td><td>(1.481)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">MedRent</td><td>8.011</td><td>10.111</td></tr>
## <tr><td style="text-align:left"></td><td>(16.927)</td><td>(13.970)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">pctWhite</td><td>87,738.750<sup>***</sup></td><td>72,584.590<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(21,213.910)</td><td>(18,038.400)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">pctPoverty</td><td>-65,160.580</td><td>-28,329.320</td></tr>
## <tr><td style="text-align:left"></td><td>(46,955.060)</td><td>(38,669.420)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Brownsville.MS</td><td>-74,321.900<sup>**</sup></td><td>-19,595.140</td></tr>
## <tr><td style="text-align:left"></td><td>(35,665.230)</td><td>(29,848.970)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">CitrusGrove.MS</td><td>-63,085.380<sup>*</sup></td><td>-16,536.970</td></tr>
## <tr><td style="text-align:left"></td><td>(33,757.230)</td><td>(27,908.010)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">JosedeDiego.MS</td><td>-24,574.030</td><td>41,689.690</td></tr>
## <tr><td style="text-align:left"></td><td>(36,087.170)</td><td>(30,171.430)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">GeorgiaJA.MS</td><td>-83,659.540<sup>**</sup></td><td>-21,745.790</td></tr>
## <tr><td style="text-align:left"></td><td>(33,968.440)</td><td>(28,569.970)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">KinlochPk.MS</td><td>-20,898.120</td><td>7,151.547</td></tr>
## <tr><td style="text-align:left"></td><td>(23,871.550)</td><td>(19,733.870)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Madison.MS</td><td>-102,752.000</td><td>-24,901.940</td></tr>
## <tr><td style="text-align:left"></td><td>(89,066.670)</td><td>(73,254.900)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Nautilus.MS</td><td>229,234.000<sup>***</sup></td><td></td></tr>
## <tr><td style="text-align:left"></td><td>(37,774.810)</td><td></td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Shenandoah.MS</td><td>99,482.560<sup>***</sup></td><td>122,292.100<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(31,097.140)</td><td>(25,991.120)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">WestMiami.MS</td><td></td><td></td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Constant</td><td>274,559.400<sup>***</sup></td><td>-5,246.435</td></tr>
## <tr><td style="text-align:left"></td><td>(50,967.110)</td><td>(142,697.300)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observations</td><td>1,584</td><td>1,584</td></tr>
## <tr><td style="text-align:left">R<sup>2</sup></td><td>0.603</td><td>0.736</td></tr>
## <tr><td style="text-align:left">Adjusted R<sup>2</sup></td><td>0.599</td><td>0.732</td></tr>
## <tr><td style="text-align:left">Residual Std. Error</td><td>113,746.600 (df = 1569)</td><td>93,070.580 (df = 1559)</td></tr>
## <tr><td style="text-align:left">F Statistic</td><td>170.158<sup>***</sup> (df = 14; 1569)</td><td>180.949<sup>***</sup> (df = 24; 1559)</td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"><em>Note:</em></td><td colspan="2" style="text-align:right"><sup>*</sup>p<0.1; <sup>**</sup>p<0.05; <sup>***</sup>p<0.01</td></tr>
## </table>#GEOID R2 = .3, MailingZip =.4, PropertyZip =.9##
## Call:
## lm(formula = SalePrice ~ ., data = miami.training %>% st_drop_geometry() %>%
## dplyr::select(-GEOID, -ID, -toPredict))
##
## Residuals:
## Min 1Q Median 3Q Max
## -302587 -51571 -2064 44957 614688
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 78136.837213698 176059.192638503 0.444
## Folio -0.000000385 0.000001255 -0.307
## Property.CityMiami Beach 276454.999110661 127451.105147057 2.169
## LotSize 16.317702062 2.038776726 8.004
## Bed 5988.517104382 5541.684530678 1.081
## Bath 5341.577560724 6854.121820066 0.779
## Stories 20516.913244497 13971.424146060 1.468
## Pool 76118.434570713 12024.746850741 6.330
## Fence -5153.231757390 7177.774007681 -0.718
## Patio 2589.646364106 6402.120172277 0.404
## ActualSqFt 69.342553528 8.107934838 8.552
## Age -682.246009530 189.026082349 -3.609
## Shore1 -4.093915075 1.292472764 -3.168
## MedHHInc 1.254048187 0.244696272 5.125
## TotalPop 4.977026127 1.842105838 2.702
## MedRent -1.208459171 18.291532168 -0.066
## pctWhite 52237.978936399 23119.019761861 2.260
## pctPoverty -26272.643845086 48485.282085386 -0.542
## Brownsville.MS -17771.098702723 37362.287052672 -0.476
## CitrusGrove.MS -19914.470114837 34995.870977921 -0.569
## JosedeDiego.MS 34037.919499548 37607.403497168 0.905
## GeorgiaJA.MS -25082.785286265 35628.510515297 -0.704
## KinlochPk.MS 23587.524677210 25417.575417248 0.928
## Madison.MS -62121.192559062 97745.969841958 -0.636
## Nautilus.MS NA NA NA
## Shenandoah.MS 134605.350370903 32631.951861755 4.125
## WestMiami.MS NA NA NA
## Pr(>|t|)
## (Intercept) 0.657284
## Folio 0.759051
## Property.CityMiami Beach 0.030329 *
## LotSize 0.00000000000000361 ***
## Bed 0.280143
## Bath 0.435989
## Stories 0.142312
## Pool 0.00000000038172082 ***
## Fence 0.472974
## Patio 0.685940
## ActualSqFt < 0.0000000000000002 ***
## Age 0.000324 ***
## Shore1 0.001588 **
## MedHHInc 0.00000036255562183 ***
## TotalPop 0.007023 **
## MedRent 0.947339
## pctWhite 0.024083 *
## pctPoverty 0.588040
## Brownsville.MS 0.634442
## CitrusGrove.MS 0.569459
## JosedeDiego.MS 0.365656
## GeorgiaJA.MS 0.481605
## KinlochPk.MS 0.353650
## Madison.MS 0.525236
## Nautilus.MS NA
## Shenandoah.MS 0.00004042762290486 ***
## WestMiami.MS NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 89360 on 923 degrees of freedom
## (294 observations deleted due to missingness)
## Multiple R-squared: 0.7519, Adjusted R-squared: 0.7454
## F-statistic: 116.5 on 24 and 923 DF, p-value: < 0.00000000000000022## Train MAE: 195610
## Test MAE: 61fitControl <- trainControl(method = "cv",
number = 100,
# savePredictions differs from book
savePredictions = TRUE)
set.seed(73506)
#No neighborhoods R2=0.788, MAE=525,277
reg.cv2 <-
train(SalePrice ~ ., data = miamiHomes.train %>%
st_drop_geometry() %>%
dplyr::select(-ActualSqFt, -TotalPop, -ID,
-MedHHInc, -toPredict),
method = "lm",
trControl = fitControl,
na.action = na.omit)
reg.cv2## Linear Regression
##
## 2066 samples
## 24 predictor
##
## No pre-processing
## Resampling: Cross-Validated (100 fold)
## Summary of sample sizes: 1568, 1568, 1567, 1568, 1568, 1568, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 88416.28 0.7556264 65775.12
##
## Tuning parameter 'intercept' was held constant at a value of TRUE#Providing Results of Cross Validation Test
reg.cv2$results %>%
knitr::kable()| intercept | RMSE | Rsquared | MAE | RMSESD | RsquaredSD | MAESD |
|---|---|---|---|---|---|---|
| TRUE | 88416.28 | 0.7556264 | 65775.12 | 25971.98 | 0.1477249 | 16997.15 |
#Creating an MAE Histogram
MAE_hist <- as.data.frame(reg.cv2$pred) %>%
mutate(ABS_error = abs(pred-obs)) %>%
group_by(Resample) %>%
summarize(MAE = mean(ABS_error, na.rm = T))
ggplot(MAE_hist, aes(x=MAE))+geom_histogram()+
labs(title="Histogram of Cross Validation MAE",
caption="Based on 100 Folds")+
theme_classic()
#Plotting Predicted Prices as a Function of Observed Prices
regCV2plot <- as.data.frame(reg.cv2$pred)
ggplot(regCV2plot,aes(obs,pred)) +
geom_point() +
stat_smooth(aes(obs, obs),
method = "lm", se = FALSE, size = 1, colour="#FA7800") +
stat_smooth(aes(obs, pred),
method = "lm", se = FALSE, size = 1, colour="#25CB10") +
labs(title="Predicted sale price as a function of observed price",
subtitle="Orange line represents a perfect prediction; Green line represents prediction",
x="Sale Price",
y="Predicted Price") +
plotTheme() + theme(plot.title = element_text(size = 18, colour = "black")) 
## [1] 2066## [1] 1584#our best model was reg.cv2
1 — Markdown: Introduction —-
##
## <table style="text-align:center"><caption><strong>Summary Statistics</strong></caption>
## <tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Statistic</td><td>N</td><td>Mean</td><td>St. Dev.</td><td>Min</td><td>Max</td></tr>
## <tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">SalePrice</td><td>2,066</td><td>405,476.400</td><td>199,741.700</td><td>12,500</td><td>1,000,000</td></tr>
## <tr><td style="text-align:left">Miami.dummy</td><td>2,066</td><td>0.953</td><td>0.212</td><td>0</td><td>1</td></tr>
## <tr><td style="text-align:left">LotSize</td><td>2,066</td><td>6,360.875</td><td>1,721.617</td><td>1,250</td><td>17,620</td></tr>
## <tr><td style="text-align:left">Age</td><td>2,066</td><td>70.954</td><td>18.186</td><td>-1</td><td>115</td></tr>
## <tr><td style="text-align:left">Stories</td><td>2,066</td><td>1.073</td><td>0.265</td><td>0</td><td>3</td></tr>
## <tr><td style="text-align:left">Bed</td><td>2,066</td><td>2.692</td><td>0.794</td><td>0</td><td>8</td></tr>
## <tr><td style="text-align:left">Bath</td><td>2,066</td><td>1.611</td><td>0.700</td><td>0</td><td>6</td></tr>
## <tr><td style="text-align:left">Pool</td><td>2,066</td><td>0.108</td><td>0.310</td><td>0</td><td>1</td></tr>
## <tr><td style="text-align:left">Fence</td><td>2,066</td><td>0.738</td><td>0.440</td><td>0</td><td>1</td></tr>
## <tr><td style="text-align:left">Patio</td><td>2,066</td><td>0.499</td><td>0.500</td><td>0</td><td>1</td></tr>
## <tr><td style="text-align:left">Shore1</td><td>2,066</td><td>7,047.549</td><td>5,248.614</td><td>88.597</td><td>26,528.540</td></tr>
## <tr><td style="text-align:left">MedRent</td><td>2,040</td><td>1,042.535</td><td>311.133</td><td>246.000</td><td>2,297.000</td></tr>
## <tr><td style="text-align:left">pctWhite</td><td>2,062</td><td>0.703</td><td>0.320</td><td>0.057</td><td>0.989</td></tr>
## <tr><td style="text-align:left">pctPoverty</td><td>2,062</td><td>0.217</td><td>0.108</td><td>0.052</td><td>0.556</td></tr>
## <tr><td style="text-align:left">Brownsville.MS</td><td>1,588</td><td>0.098</td><td>0.298</td><td>0.000</td><td>1.000</td></tr>
## <tr><td style="text-align:left">CitrusGrove.MS</td><td>1,588</td><td>0.115</td><td>0.319</td><td>0.000</td><td>1.000</td></tr>
## <tr><td style="text-align:left">JosedeDiego.MS</td><td>1,588</td><td>0.129</td><td>0.335</td><td>0.000</td><td>1.000</td></tr>
## <tr><td style="text-align:left">GeorgiaJA.MS</td><td>1,588</td><td>0.133</td><td>0.340</td><td>0.000</td><td>1.000</td></tr>
## <tr><td style="text-align:left">KinlochPk.MS</td><td>1,588</td><td>0.196</td><td>0.397</td><td>0.000</td><td>1.000</td></tr>
## <tr><td style="text-align:left">Madison.MS</td><td>1,588</td><td>0.001</td><td>0.035</td><td>0.000</td><td>1.000</td></tr>
## <tr><td style="text-align:left">Nautilus.MS</td><td>1,588</td><td>0.061</td><td>0.240</td><td>0.000</td><td>1.000</td></tr>
## <tr><td style="text-align:left">Shenandoah.MS</td><td>1,588</td><td>0.243</td><td>0.429</td><td>0.000</td><td>1.000</td></tr>
## <tr><td style="text-align:left">WestMiami.MS</td><td>1,588</td><td>0.024</td><td>0.153</td><td>0.000</td><td>1.000</td></tr>
## <tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr></table>
##
## <table style="text-align:center"><caption><strong>Summary Statistics</strong></caption>
## <tr><td colspan="1" style="border-bottom: 1px solid black"></td></tr><tr><td>asis</td></tr>
## <tr><td colspan="1" style="border-bottom: 1px solid black"></td></tr></table>
##
## <table style="text-align:center"><caption><strong>Summary Statistics</strong></caption>
## <tr><td colspan="1" style="border-bottom: 1px solid black"></td></tr><tr><td>FALSE</td></tr>
## <tr><td colspan="1" style="border-bottom: 1px solid black"></td></tr></table>
# — Markdown: Method —-
2 — Markdown: Results —-
# Is there a spatial correlation of errors?
# get index for training sample
inTrain <- caret::createDataPartition(
y = miamiHomes.train$SalePrice,
p = .60, list = FALSE)
# split data into training and test
miami.training <- miamiHomes.train[inTrain,]
miami.test <- miamiHomes.train[-inTrain,]
#this is the dataset and variables we used in regCV2
#however I had to drop GEOID since there was a levels error
finaltraining <- lm(SalePrice ~ ., data = miami.training %>%
st_drop_geometry() %>%
dplyr::select(-GEOID, -ID,
-TotalPop, -MedHHInc, -toPredict))
miami.test <-
miami.test %>%
mutate(Regression = "Baseline Regression",
SalePrice.Predict = predict(finaltraining, miami.test),
SalePrice.Error = SalePrice.Predict - SalePrice,
SalePrice.AbsError = abs(SalePrice.Predict - SalePrice),
SalePrice.APE = (abs(SalePrice.Predict - SalePrice)) / SalePrice.Predict)## Warning: Problem with `mutate()` input `SalePrice.Predict`.
## ℹ prediction from a rank-deficient fit may be misleading
## ℹ Input `SalePrice.Predict` is `predict(finaltraining, miami.test)`.## Warning in predict.lm(finaltraining, miami.test): prediction from a rank-
## deficient fit may be misleadingk_nearest_neighbors = 5
#prices
coords <- st_coordinates(st_centroid(miamiHomesClean.sf))## Warning in st_centroid.sf(miamiHomesClean.sf): st_centroid assumes attributes
## are constant over geometries of x# k nearest neighbors
neighborList <- knn2nb(knearneigh(coords, k_nearest_neighbors))## Warning in knearneigh(coords, k_nearest_neighbors): knearneigh: identical points
## foundspatialWeights <- nb2listw(neighborList, style="W")
miamiHomesClean.sf$lagPrice <- lag.listw(spatialWeights, miamiHomesClean.sf$SalePrice)
miami.test.lag <- drop_na(miami.test)
#errors
coords.test <- st_coordinates(st_centroid(miami.test.lag))## Warning in st_centroid.sf(miami.test.lag): st_centroid assumes attributes are
## constant over geometries of xneighborList.test <- knn2nb(knearneigh(coords.test, k_nearest_neighbors))## Warning in knearneigh(coords.test, k_nearest_neighbors): knearneigh: identical
## points foundspatialWeights.test <- nb2listw(neighborList.test, style="W")
miami.test.lag$lagPriceError <- lag.listw(spatialWeights.test, miami.test.lag$SalePrice.AbsError)
#this is breaking because of annotation_map & geom_sf miami base
ggplot(miamiHomesClean.sf, aes(x=lagPrice, y=SalePrice)) +
geom_point(colour = "#FA7800") +
geom_smooth(method = "lm", se = FALSE, colour = "#25CB10") +
labs(title = "Price as a function of the spatial lag of price",
caption = "Public Policy Analytics, Figure 6.6",
x = "Spatial lag of price (Mean price of 5 nearest neighbors)",
y = "Sale Price") +
plotTheme()## `geom_smooth()` using formula 'y ~ x'
ggplot(miami.test.lag, aes(x=lagPriceError, y=SalePrice)) +
geom_point(colour = "#FA7800") +
geom_smooth(method = "lm", se = FALSE, colour = "#25CB10") +
labs(title = "Error as a function of the spatial lag of price",
caption = "",
x = "Spatial lag of errors (Mean error of 5 nearest neighbors)",
y = "Sale Price") +
plotTheme()## `geom_smooth()` using formula 'y ~ x'
#Moran's I Test
moranTest <- moran.mc(miami.test.lag$SalePrice.AbsError,
spatialWeights.test, nsim = 999, na.action=na.exclude)
ggplot(as.data.frame(moranTest$res[c(1:999)]), aes(moranTest$res[c(1:999)])) +
geom_histogram(binwidth = 0.01) +
geom_vline(aes(xintercept = moranTest$statistic), colour = "#FA7800",size=1) +
scale_x_continuous(limits = c(-1, 1)) +
labs(title="Observed and permuted Moran's I",
subtitle= "Observed Moran's I in orange",
x="Moran's I",
y="Count",
caption="Public Policy Analytics, Figure 6.8") +
plotTheme()## Warning: Removed 2 rows containing missing values (geom_bar).
| GEOID | meanPrice | meanPrediction | meanMAE |
|---|---|---|---|
| 12086003001 | 915000.0 | 268327.05 | 646672.946 |
| 12086005202 | 700000.0 | 445685.61 | 254314.392 |
| 12086004304 | 307000.0 | 525805.20 | 218805.197 |
| 12086003912 | 539000.0 | 577841.20 | 211835.504 |
| 12086003004 | 575000.0 | 437675.04 | 137324.962 |
| 12086003915 | 591785.7 | 688403.10 | 132921.677 |
| 12086006601 | 624993.1 | 522584.59 | 126780.120 |
| 12086005102 | 436571.4 | 316573.29 | 120398.032 |
| 12086002004 | 150000.0 | 268285.44 | 118285.438 |
| 12086004102 | 700000.0 | 584514.34 | 115485.658 |
| 12086005410 | 340000.0 | 451302.58 | 111302.580 |
| 12086006503 | 434000.0 | 459507.25 | 109272.858 |
| 12086003906 | 794950.0 | 771691.90 | 107937.653 |
| 12086006702 | 690461.5 | 603962.64 | 105641.596 |
| 12086002900 | 238000.0 | 336254.91 | 104279.592 |
| 12086006403 | 552071.4 | 512562.37 | 97561.292 |
| 12086002201 | 437045.5 | 444508.34 | 96206.119 |
| 12086005407 | 419100.0 | 426226.95 | 92830.740 |
| 12086003916 | 602333.3 | 690492.62 | 88159.283 |
| 12086006900 | 494965.0 | 515227.53 | 86630.053 |
| 12086003003 | 358750.0 | 442894.40 | 84144.398 |
| 12086002202 | 329363.9 | 317885.04 | 81962.040 |
| 12086004000 | 776714.3 | 751661.83 | 78755.202 |
| 12086006402 | 471170.6 | 466438.30 | 69228.772 |
| 12086005104 | 307500.0 | 355688.48 | 69206.464 |
| 12086005600 | 378323.5 | 380727.01 | 66111.009 |
| 12086006401 | 416208.3 | 456677.65 | 65606.356 |
| 12086001501 | 149823.5 | 96667.49 | 65155.251 |
| 12086002003 | 215557.1 | 251433.27 | 63769.424 |
| 12086005001 | 315233.3 | 360172.70 | 62695.229 |
| 12086001802 | 204153.8 | 219469.02 | 62282.077 |
| 12086002600 | 370760.0 | 332049.58 | 61184.751 |
| 12086005801 | 344769.0 | 349191.94 | 60101.193 |
| 12086004106 | 812925.0 | 814527.02 | 59134.433 |
| 12086005302 | 245600.0 | 303511.05 | 57911.052 |
| 12086006504 | 452777.8 | 506102.72 | 57820.995 |
| 12086002501 | 256950.0 | 252675.70 | 57534.074 |
| 12086004902 | 332882.4 | 342138.81 | 57330.224 |
| 12086006501 | 463807.7 | 479835.59 | 55738.458 |
| 12086001904 | 215546.2 | 213373.50 | 54032.128 |
| 12086001801 | 198980.0 | 196910.64 | 51976.306 |
| 12086001901 | 187181.8 | 205221.51 | 50874.559 |
| 12086005201 | 250000.0 | 300260.98 | 50260.979 |
| 12086005405 | 291500.0 | 317920.50 | 49823.456 |
| 12086002402 | 237066.7 | 275337.91 | 49122.809 |
| 12086001903 | 227722.2 | 237934.07 | 49075.425 |
| 12086002300 | 234197.4 | 213052.21 | 46524.769 |
| 12086005502 | 331000.0 | 332577.31 | 43788.613 |
| 12086005802 | 338025.7 | 335565.40 | 43297.792 |
| 12086005701 | 332344.4 | 315157.65 | 39424.029 |
| 12086005704 | 347100.0 | 333505.12 | 37294.808 |
| 12086005002 | 312454.5 | 340536.20 | 36677.606 |
| 12086002403 | 278757.1 | 315030.59 | 36273.451 |
| 12086005406 | 319500.0 | 286922.37 | 32577.630 |
| 12086490100 | 348500.0 | 345176.76 | 29316.631 |
| 12086005501 | 313000.0 | 292218.20 | 28602.688 |
| 12086005403 | 300000.0 | 290351.41 | 20285.762 |
| 12086002502 | 235625.0 | 216167.54 | 19457.458 |
| 12086002404 | 237833.3 | 227770.79 | 10062.541 |
| 12086003602 | 371000.0 | 364975.68 | 6024.317 |
| 12086003100 | 330000.0 | 324816.59 | 5183.408 |
| 12086005103 | 265000.0 | 261525.08 | 3474.923 |
| 12086001301 | 503615.8 | NaN | NaN |
| 12086001302 | 575275.0 | NaN | NaN |
| 12086001401 | 194180.0 | NaN | NaN |
| 12086001402 | 225000.0 | NaN | NaN |
| 12086002001 | 189940.0 | NaN | NaN |
| 12086002100 | 758181.8 | NaN | NaN |
| 12086006301 | 392666.7 | NaN | NaN |
| 12086006302 | 409836.8 | NaN | NaN |
| 12086006801 | 745872.7 | NaN | NaN |
| 12086006802 | 759500.0 | NaN | NaN |
| 12086007001 | 347500.0 | NaN | NaN |
| 12086007002 | 391250.0 | NaN | NaN |
| 12086007101 | 559285.7 | NaN | NaN |
| 12086007104 | 545000.0 | NaN | NaN |
| 12086007200 | 353516.7 | NaN | NaN |
| 12086007300 | 735517.6 | NaN | NaN |
## [1] 37283## Linear Regression
##
## 403 samples
## 23 predictor
##
## No pre-processing
## Resampling: Cross-Validated (100 fold)
## Summary of sample sizes: 399, 400, 398, 399, 398, 398, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 130147.8 0.7933946 93060.55
##
## Tuning parameter 'intercept' was held constant at a value of TRUE## Linear Regression
##
## 414 samples
## 25 predictor
##
## No pre-processing
## Resampling: Cross-Validated (100 fold)
## Summary of sample sizes: 291, 290, 290, 290, 290, 290, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 98912.42 0.709759 82492.1
##
## Tuning parameter 'intercept' was held constant at a value of TRUE## Linear Regression
##
## 414 samples
## 25 predictor
##
## No pre-processing
## Resampling: Cross-Validated (100 fold)
## Summary of sample sizes: 291, 290, 290, 290, 290, 290, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 98912.42 0.709759 82492.1
##
## Tuning parameter 'intercept' was held constant at a value of TRUE| intercept | RMSE | Rsquared | MAE | RMSESD | RsquaredSD | MAESD |
|---|---|---|---|---|---|---|
| TRUE | 130147.8 | 0.7933946 | 93060.55 | 354594.9 | 0.2778949 | 210570.7 |
kable(miamiRichLM$results)| intercept | RMSE | Rsquared | MAE | RMSESD | RsquaredSD | MAESD |
|---|---|---|---|---|---|---|
| TRUE | 98912.42 | 0.709759 | 82492.1 | 52113.41 | 0.271611 | 39852.27 |